Group identities on units of group algebras
type: Item
instance of: scholarly article
title: Group identities on units of group algebras
zbMATH Open document ID: 0958.16033
author: Antonio Giambruno
author: Sudarshan K. Sehgal
author: Angela Valenti
published in: Journal of Algebra
publication date: 2001-01-18T00:00:00Z
review text: Let \(U\) be the group of units of the group algebra \(FG\), where \(G\) is a group and \(F\) is a field. This paper is concerned with determining when \(U\) satisfies a group identity. If \(G\) is torsion, then this question was settled in recent years, thereby yielding an affirmative solution to Hartley's problem. Here, the authors deal with groups that are nilpotent modulo torsion elements and they offer a full characterization when \(F\) is infinite. In particular, if \(p\geq 0\) is the characteristic of the field, then they show that the set of all \(p\)-elements \(P\) must necessarily form a normal subgroup of \(G\), and that the nature of the answer splits into two cases according to whether \(P\) has bounded exponent or not.
Mathematics Subject Classification ID: 16U60
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 20C07
Mathematics Subject Classification ID: 20F50
Mathematics Subject Classification ID: 20F18
Mathematics Subject Classification ID: 20E07
zbMATH DE Number: 1441820
zbMATH Keywords: group algebras
zbMATH Keywords: unit groups
zbMATH Keywords: group identities
zbMATH Keywords: nilpotent groups
zbMATH Keywords: groups of bounded exponent
zbMATH Keywords: normal subgroups
zbMATH Keywords: \(p\)-elements
reviewed by: D. S. Passman
MaRDI profile type: Publication
full work available at URL: jabr.1999.8203
OpenAlex ID: W1976656516
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DOI: 10.1006/JABR.1999.8203
description: scientific article; zbMATH DE number 1441820